Relatively slender spindle shafts of substantial length driving a chuck at one end from a belt sheave at the other develop a resilient torsional deflection. The masses represented by the chuck and the drive sheave at the opposite ends of the slender shaft have a vibratory resonance frequency in torsion. When a work piece held by the chuck engages a cutting tool, or vice versa, the torsional flexibility of the shaft results in the tendency for the tool to cut unevenly in a chattering action as the cutting torque causes the spindle to wind up and then release in small amounts at the resonant frequency as the cutting proceeds. The result is an undesireable roughness in the cut surface. This problem has been encountered in the operation of a machine constructed as shown in my U.S. Pat. No. 3,470,789, where the spindle of a drill press functions as the spindle of a lathe and also of a milling machine.